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Share-based awards (Tables)
9 Months Ended
Sep. 30, 2021
Share-based Payment Arrangement [Abstract]  
Schedule of Share Option Activity The following table summarizes option activity for the nine months ended September 30, 2021:
 Options
Outstanding
Number of Shares 
Weighted
Average
Exercise
Price
Weighted
Average
Remaining
Contractual
Life
Outstanding at December 31, 2020553,746 $108.53 4.86
Assumed through business combinations (a)
2,177,130 $108.78 
Granted100,299 $177.76 
Exercised(913,743)$113.87 
Canceled/expired(32,784)$132.25 
Outstanding at September 30, 20211,884,648 $109.50 5.66
Exercisable at September 30, 20211,095,429 $90.80 4.72

(a) Represents stock options issued as replacement awards in connection with the Merger.
Schedule of Weighted Average Fair Values and Assumptions Used The weighted average grant date fair values and assumptions used were as follows:
Nine Months Ended
September 30, 2021September 30, 2020
Weighted average grant date fair value$49.15 $42.43 
Assumptions:  
Expected volatility30 %30 %
Dividend yield— %— %
Risk-free interest rate0.78 %0.57 %
Expected life5 years5 years
The weighted average fair values on the date of the Merger and assumptions used were as follows:
July 1, 2021
Weighted average grant date fair value$107.21 
Assumptions:
Expected volatility30 %
Dividend yield— %
Risk-free interest rate0.56 %
Expected life3.5 years
Schedule of RSU and PSU Activity The following table summarizes RSU and PSU activity for the nine months ended September 30, 2021:
  
PSU
Outstanding
Number of
Shares
 
PSU
Weighted
Average Grant Date
Fair Value
 
RSU
Outstanding
Number of
Shares
 
RSU
Weighted
Average Grant Date
Fair Value
Outstanding at December 31, 2020159,641 $137.64 341,424 $145.77 
Assumed through business combinations (a)
— $— 589,517 $206.71 
Granted55,444 $177.77 159,796 $210.64 
Shares vested(44,132)$115.61 (441,328)$186.03 
Forfeited(4,777)$115.61 (48,441)$180.74 
Outstanding at September 30, 2021166,176 $159.11 600,968 $190.56 

(a) Represents RSUs issued as replacement awards in connection with the Merger.
Schedule of Non-cash Stock Compensation Expense Non-cash stock compensation expense for the three and nine months ended September 30, 2021 and September 30, 2020 has been allocated as follows:
Three Months EndedNine Months Ended
September 30, 2021September 30, 2020September 30, 2021September 30, 2020
(in thousands)(in thousands)
Direct costs$8,787 $2,284 $13,822 $6,472 
Selling, general and administrative17,568 4,687 27,133 13,685 
Transaction and integration-related expenses73,836 — 73,836 — 
 $100,191 $6,971 $114,791 $20,157